Interim manager Roberto Di Matteo believes Chelsea have every chance of claiming a UEFA Champions League spot with just seven games remaining.
The West Londoners won their sixth game out of eight since the Italian took over from Andre Villas-Boas at Stamford Bridge with a 4-2 success at Aston Villa on Saturday.
Daniel Sturridge and Branislav Ivanovic earned them a 2-0 lead only for Villa to rally through goals from James Collins and Eric Lichaj.
But Ivanovic's second of the game and then Fernando Torres' first league goal for six months capped off an impressive display for the Blues.
The three points kept the pressure on Arsenal and Tottenham above them and with crunch games against the Gunners as well as Newcastle and Liverpool to come before the end of the season, Di Matteo believes it's still all to play for.
He said: "We've always said we will try to the end of the season. We are playing catch-up. That is our situation.
"The only thing we can do is try to win our games and keeping putting pressure on the top four.
"The top four is certainly a priority for us. It is crucial for us to finish there."
And on the victory at Villa Park, Di Matteo added: "Apart from five minutes when Villa scored twice, we controlled the game very well, and had one or two chances to score more goals.
"It was great spirit by the team to react to that double setback because it could have gone the other way as well. We could have capitulated.
"The players found an extra gear at the end but that is the quality of these players.
"We have that in the squad and we showed that again but I'm so happy about the spirit that we are showing at the moment.
"We don't give up and we believe to the end of the game."